Recommend book to follow Introduction to Analysis by Rosenlicht

I am trying to build a great foundation in analysis before moving into functional analysis, ode and tensor calc( planning on graduate school in computational fluid mechanics ). I love the style of Rosenlichts text. What's the best book to take it to the next level? I seek something very strong in analysis of functions of several real variables and vector analysis.... Any suggestions? Does principles of mathematical analysis by rudin cover multivariate and vector functions?